Subgroups — #15831992

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123468	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
4	#13113615	C₂	1	4	yes	maximal, complemented
5	#13113611	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113608	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113606	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113583	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#431	C₂²	1	1	yes	characteristic
12	C₁₃×#423	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	#11718787	—	2	1	no	—
15	M₁₆×Dic₁₃	—	2	1	no	—
16	C₂×#88060	—	2	1	no	—
17	C₂×C₈×Dic₁₃	—	2	1	no	—
18	#11718586	C₂²	1	1	yes	characteristic
19	#11718585	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	#11718496	—	2	1	no	—
22	#11718496	C₂²	1	2	yes	—
23	#11718494	—	2	1	no	—
24	#11718494	—	2	1	no	—
25	#11718494	—	2	1	no	—
26	#11718494	C₄	1	2	yes	—
27	#11718494	C₂²	1	2	yes	—
28	#11718494	C₂²	1	2	yes	—
29	#11718494	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
32	#11718379	C₄	1	2	yes	—
33	#11718346	C₂²	1	2	yes	—
34	C₄×C₈×D₁₃	C₂²	1	2	yes	—
35	C₁₃×#335	C₂²	1	4	yes	complemented
36	#11718072	C₂²	1	4	yes	complemented
37	#11718072	C₂²	1	4	yes	complemented
38	#11718050	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	—	2	1	no	—
43	C₂²×C₈×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
48	C₂×#6099	—	2	1	no	—
49	C₂²×#1055	—	2	1	no	—
50	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	D₄	1	1	yes	characteristic
54	C₄²×D₁₃	D₄	1	1	yes	characteristic
55	C₄²×D₁₃	Q₈	1	1	yes	characteristic
56	C₄²×D₁₃	Q₈	1	1	yes	characteristic
57	C₄²×D₁₃	C₂³	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊C₈	—	2	1	no	—
60	C₁₃×C₄⋊C₈	—	2	1	no	—
61	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₁₃	C₂³	1	2	yes	—
66	C₂²⋊#1055	C₂×C₄	1	2	yes	—
67	#88060	—	2	2	no	—
68	#88060	—	2	2	no	—
69	#88060	—	2	2	no	—
70	#88060	—	2	2	no	—
71	#88060	C₂×C₄	1	4	yes	—
72	#88055	—	2	2	no	—
73	#88054	C₂×C₄	1	4	yes	—
74	C₈×Dic₁₃	—	2	2	no	—
75	C₈×Dic₁₃	—	2	2	no	—
76	C₈×Dic₁₃	—	2	2	no	—
77	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
78	C₄⋊#1055	—	2	1	no	—
79	C₄⋊#1055	—	2	1	no	—
80	C₄⋊#1055	C₂×C₄	1	2	yes	—
81	C₄⋊#1055	C₂³	1	2	yes	—
82	C₄⋊#1055	C₂³	1	2	yes	—
83	C₄×#1055	C₂³	1	2	yes	—
84	#17803	—	13	1	no	maximal, Sylow
85	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	—	2	2	no	—
93	C₂×C₄×D₁₃	—	2	2	no	—
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
108	C₁₃×M₁₆	—	4	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	4	2	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
129	#6099	—	4	2	no	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	4	2	no	—
133	C₂×#1055	C₂²×C₄	1	4	yes	—
134	C₈×D₁₃	—	2	8	no	—
135	#2920	—	13	1	no	—
136	C₂×#431	—	13	1	no	—
137	C₂×#431	—	13	1	no	—
138	#1572	—	13	4	no	—
139	#1571	—	13	1	no	—
140	#1571	D₁₃	1	1	yes	characteristic, complemented
141	#1570	—	13	1	no	—
142	#1570	—	13	1	no	—
143	#1564	—	13	4	no	—
144	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×D₁₃	—	2	2	no	—
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	—	4	1	no	—
148	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#135	1	2	yes	—
156	C₂×C₄×C₁₃	#135	1	2	yes	—
157	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
160	C₂×Dic₁₃	—	2	2	no	—
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	1	no	—
172	C₄×D₁₃	—	2	1	no	—
173	C₄×D₁₃	—	2	1	no	—
174	C₄×D₁₃	—	2	1	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	4	1	no	—
181	C₄×D₁₃	—	4	1	no	—
182	C₄×D₁₃	#131	1	4	yes	—
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	4	2	no	—
186	#1055	—	2	4	no	—
187	#1055	—	4	2	no	—
188	#1055	—	4	2	no	—
189	C₂²×C₄²	—	13	1	no	—
190	#432	—	13	2	no	—
191	#432	—	26	1	no	—
192	#431	—	13	1	no	—
193	#431	—	13	2	no	—
194	#431	—	13	2	no	—
195	#431	—	13	2	no	—
196	#431	—	13	2	no	—
197	#431	—	13	2	no	—
198	#431	—	13	2	no	—
199	#431	—	26	1	no	—
200	#431	—	26	1	no	—
201	#431	—	26	1	no	—
202	#431	C₂×D₁₃	1	1	yes	characteristic
203	#423	—	13	1	no	—
204	#423	C₂×D₁₃	1	1	yes	characteristic
205	C₂×C₄⋊C₈	—	13	2	no	—
206	C₂×C₄⋊C₈	—	13	1	no	—
207	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
208	#407	—	26	1	no	—
209	C₂×C₂²⋊C₈	—	13	2	no	—
210	C₂×C₂²⋊C₈	—	26	1	no	—
211	C₄×M₁₆	—	26	1	no	—
212	C₂×C₄×C₈	—	13	2	no	—
213	C₂×C₄×C₈	—	26	1	no	—
214	#335	—	13	4	no	—
215	#335	C₂×D₁₃	1	4	yes	complemented
216	#334	—	13	4	no	—
217	#334	—	13	4	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	#427	1	2	yes	—
221	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₂×D₁₃	—	2	1	no	—
223	C₂×D₁₃	—	2	1	no	—
224	C₂×D₁₃	—	2	1	no	—
225	C₂×D₁₃	—	2	1	no	—
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	—	4	4	no	—
228	C₂×D₁₃	#424	1	2	yes	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	#427	1	2	yes	—
233	C₄×C₁₃	C₂×#131	1	2	yes	—
234	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
235	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
236	Dic₁₃	—	2	1	no	—
237	Dic₁₃	—	2	1	no	—
238	Dic₁₃	—	2	1	no	—
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	#424	1	2	yes	—
241	Dic₁₃	#430	1	2	yes	—
242	C₂³×C₄	—	13	1	no	—
243	C₂³×C₄	—	13	1	no	—
244	C₂³×C₄	—	13	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	26	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	13	4	no	—
249	C₂²×C₈	—	26	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	13	4	no	—
265	C₄⋊C₈	—	13	2	no	—
266	C₄⋊C₈	—	13	2	no	—
267	C₄⋊C₈	—	13	2	no	—
268	C₄⋊C₈	—	26	1	no	—
269	C₄⋊C₈	—	26	1	no	—
270	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
271	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
272	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
273	C₂²⋊C₈	—	13	2	no	—
274	C₂²⋊C₈	—	13	4	no	—
275	C₂²⋊C₈	—	26	2	no	—
276	C₂²⋊C₈	—	26	2	no	—
277	C₂²⋊C₈	—	26	2	no	—
278	C₂²⋊C₈	—	26	2	no	—
279	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
280	#97	—	26	2	no	—
281	C₄×C₈	—	13	4	no	—
282	C₄×C₈	—	13	2	no	—
283	C₄×C₈	—	26	2	no	—
284	C₄×C₈	—	26	2	no	—
285	C₄×C₈	—	26	2	no	—
286	C₄×C₈	C₂²×D₁₃	1	2	yes	—
287	C₂×C₁₃	—	2	2	no	—
288	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
291	D₁₃	—	2	2	no	—
292	D₁₃	—	4	1	no	—
293	C₂⁴	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	26	4	no	—
310	C₂²×C₄	—	26	2	no	—
311	C₂²×C₄	—	26	2	no	—
312	C₂²×C₄	—	52	2	no	—
313	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	52	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	13	4	no	—
322	C₂×C₈	—	26	8	no	—
323	C₂×C₈	—	26	2	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	52	2	no	—
326	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
327	C₄²	—	13	1	no	—
328	C₄²	—	13	1	no	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
340	C₄²	D₄×D₁₃	1	1	yes	characteristic
341	C₄²	Q₈×D₁₃	1	1	yes	characteristic
342	C₄²	C₂³×D₁₃	1	1	yes	characteristic
343	C₁₃	#17803	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	13	1	no	—
345	C₂³	—	13	1	no	—
346	C₂³	—	26	2	no	—
347	C₂³	—	26	2	no	—
348	C₂³	—	52	1	no	—
349	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	13	1	no	—
353	C₂×C₄	—	13	1	no	—
354	C₂×C₄	—	13	4	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	26	1	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	1	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	52	1	no	—
374	C₂×C₄	—	52	1	no	—
375	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₄	#88166	1	2	yes	—
379	C₂×C₄	#88173	1	2	yes	—
380	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	26	4	no	—
387	C₈	—	52	2	no	—
388	C₈	—	52	2	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	13	2	no	—
392	C₂²	—	26	1	no	—
393	C₂²	—	26	1	no	—
394	C₂²	—	26	1	no	—
395	C₂²	—	26	1	no	—
396	C₂²	—	26	1	no	—
397	C₂²	—	52	4	no	—
398	C₂²	#11718541	1	2	yes	—
399	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	13	2	no	—
404	C₄	—	13	2	no	—
405	C₄	—	26	1	no	—
406	C₄	—	26	1	no	—
407	C₄	—	26	1	no	—
408	C₄	—	26	1	no	—
409	C₄	#11718541	1	2	yes	—
410	C₄	D₁₃×#131	1	2	yes	—
411	C₄	C₂×#88166	1	1	yes	characteristic
412	C₄	C₂×#88173	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	26	2	no	—
415	C₂	—	52	1	no	—
416	C₂	D₁₃×#424	1	1	yes	characteristic
417	C₂	C₂×#11718541	1	1	yes	characteristic
418	C₂	D₁₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1571	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1571	D₁₃
hypocenter	C₁₃	#17803
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #13113615	C₂	semidirect
5. #13113611	C₂	semidirect
6. #13113608	C₂	semidirect
7. #13113606	C₂	semidirect
8. #13113583	C₂	semidirect
9. C₁₃×#1571	C₂	semidirect
35. C₁₃×#335	C₂²	semidirect
36. #11718072	C₂²	semidirect
37. #11718072	C₂²	semidirect
38. #11718050	C₂²	semidirect
140. #1571	D₁₃	semidirect
215. #335	C₂×D₁₃	semidirect
343. C₁₃	#17803	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13123468	2
C₂×#11718494	2
D₁₃×#431	2
#13113615	2
#13113611	2
#13113608	2
#13113606	2
#13113583	2
C₁₃×#1571	2
#17803	13